To obtain an adhesive composition useful for wrapping retort food or the like, having an enhanced graft efficiency, capable of omitting purification process, and having high retort resistance, by graft modification of a polyolefin- based resin in the presence of a styrene-based monomer.

This composition, which contains a polyolefin resin as one of its base materials is obtained by graft polymerization, to (A) a polyolefin- based resin, of (B) a carboxylic acid (anhydride) having polymerizable unsaturated bond(s) [e.g. maleic acid (anhydride)] in the presence of (C) a styrene-based monomer, in a molten state, for example, at a weight ratio (B+C)/A of 0.01 to 0.3 and a molar ratio B/C of 0.05-1.